Home care vehicle routing problem with chargeable overtime and strict and soft preference matching

A new scheduling problem arising in the home care context is addressed, whose novelty with respect to the literature lies in the way overtime is paid. In this problem, some clients are willing to pay a higher fee to cover the additional overtime cost, if such overtime is incurred because a caregiver works extra time with the client to preserve continuity of care. These overtime hours charged to clients unburden the company, which no longer has to balance between cost and continuity of care in a traditional way. The problem is also studied in a context that includes preferences expressed by both clients and caregivers. Strict preferences must be respected with a high priority, while soft preferences increase the satisfaction and should be preferably respected. We formalize the problem as a Mixed Integer Linear Problem and also propose a cluster-based decomposition to solve real-life instances. The problem is inspired by the real case study of a provider operating in the USA. Numerical results validate the model and confirm the capability of the decomposition approach to deal with real-life instances.